Question

Am o problema la matrici clasa a 11 -a .
Imagine atasata.

Answer 1

Răspuns:

$S=\displaystyle\sum_{k=1}^nA_k=\begin{pmatrix}\displaystyle\sum_{k=1}^nk & \displaystyle\sum_{k=1}^nk^2 & \displaystyle\sum_{k=1}^nk(1+k)\\\displaystyle\sum_{k=1}^n(2k-1) & 0 & \displaystyle\sum_{k=1}^n(3k-2)}\end{pmatrix}=\\=\begin{pmatrix}S_1 & S_2 & S_3\\S_4 & 0 & S_5\end{pmatrix}$

Se folosesc sumele cunoscute de la inducția din clasa a IX-a. Avem

$S_1=\dfrac{n(n+1)}{2}$

$S_2=\dfrac{n(n+1)(2n+1)}{6}$

$S_3=\displaystyle\sum_{k=1}^n(k+k^2)=\sum_{k=1}^nk+\sum_{k=1}^nk^2=\dfrac{n(n+1)}{2}+\dfrac{n(n+1)(2n+1)}{6}$

și se mai fac calculele

$S_4=n^2$

$S_5=3\displaystyle\sum_{k=1}^nk-2n=\dfrac{3n(n+1)}{2}-2n$

Explicație pas cu pas: